The transmission of turbulent boundary layer unsteady pressure and shear stress through a viscoelastic layer

Abstract

The transmission of unsteady pressure and shear stress, generated by a turbulent boundary layer in water, through a viscoelastic layer backed by a rigid plate is investigated. Analytical models are used to estimate the unsteady pressure and shear stress from 10 to 1000 Hz for a flat plate boundary layer with zero pressure gradient. Additionally, models for the transfer of the unsteady pressures and shear stress through the viscoelastic layer are developed. The models are used to predict the unsteady pressure fluctuations, or flow noise, which would be seen by a finite size sensor embedded under the elastomer layer. The unsteady pressure levels are found to be 20 dB greater than the unsteady shear stress levels across all frequency ranges computed, in agreement with recent measurements. The unsteady pressure transfer functions have a peak at the shear wavenumber and are larger than the shear stress transfer magnitudes from 10 to 50 Hz. The unsteady shear stress transfer functions have a peak at the acoustic wavenumber and are larger than the pressure transfer magnitudes from 50 to 1000 Hz. Over the frequency range examined, the unsteady pressures were found to be the dominant contributor to the sensor flow noise due to the considerably larger magnitude of the unsteady pressures on the top of the viscoelastic layer.